Time dilation does affect the rate at which clocks tick, both in the presence of gravity and through relative motion. However, it does not directly change the frequency of sound waves or affect the pitch of a person's voice.
Time dilation refers to the phenomenon where time appears to pass at different rates for observers in different gravitational fields or in relative motion. In the presence of gravity, as predicted by Einstein's general theory of relativity, clocks closer to a massive object will tick slower compared to clocks further away. Similarly, when objects are in motion relative to each other, time dilation occurs, and clocks in motion appear to tick slower from the perspective of a stationary observer.
While time dilation affects the passage of time, it does not directly alter the frequency of sound waves or affect the fundamental properties of a person's voice, such as their pitch. The frequency of sound waves is determined by the rate at which a source vibrates, which remains constant regardless of time dilation effects. Therefore, time dilation does not result in deeper or higher-pitched voices.
However, it's worth noting that changes in gravitational fields can have an indirect impact on sound. In environments with strong gravitational fields, such as near a black hole, the gravitational field can cause a shift in the frequency of light and other electromagnetic waves. This phenomenon is known as gravitational redshift. In extreme cases, such as near the event horizon of a black hole, the gravitational redshift can significantly affect the frequency of light, but the effect on sound waves would be negligible since their wavelengths are much larger than those of light.
In summary, while time dilation affects the passage of time, it does not directly alter the frequency of sound waves or change the overall pitch of a person's voice.